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Image annotation is usually formulated as a multi-label semi-supervised learning problem. Traditional graph-based methods only utilize the data (images) graph induced from image similarities, while ignore the label (semantic terms) graph induced from label correlations of a multi-label image data set. In this paper, we propose a novel Bi-relational Graph (BG) model that comprises both the data graph and the label graph as subgraphs, and connect them by an additional bipartite graph induced from label assignments. By considering each class and its labeled images as a semantic group, we perform random walk on the BG to produce group-to-vertex relevance, including class-to-image and class-to-class relevances. The former can be used to predict labels for unannotated images, while the latter are new class relationships, called as Causal Relationships (CR), which are asymmetric. CR is learned from input data and has better semantic meaning to enhance the label prediction for unannotated images. We apply the proposed approaches to automatic image annotation and semantic image retrieval tasks on four benchmark multi-label image data sets. The superior performance of our approaches compared to state-of-the-art multi-label classification methods demonstrate their effectiveness.